Question: Simplify the following expression: $ r = \dfrac{7}{10} + \dfrac{-6p}{p + 1} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{p + 1}{p + 1}$ $ \dfrac{7}{10} \times \dfrac{p + 1}{p + 1} = \dfrac{7p + 7}{10p + 10} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-6p}{p + 1} \times \dfrac{10}{10} = \dfrac{-60p}{10p + 10} $ Therefore $ r = \dfrac{7p + 7}{10p + 10} + \dfrac{-60p}{10p + 10} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{7p + 7 - 60p}{10p + 10} $ $r = \dfrac{-53p + 7}{10p + 10}$